Introduce batch live-check infrastructure and implementations. Add BatchCheckRequest and LivePlugin::supports_batch_check/batch_check API; Monitor uses BatchLiveCache and batch_verdict to prefilter rooms (platform-level checks + caching and fast rotation). RoomsActor gains PlatformUrls. Implement batch_check for Picarto (explore pagination) and Twitch (GQL batching with auth retry). Other fixes: Douyu auth-failure detection and key invalidation + retry, Inke optional response handling, streamlink runtime tweaks for yt-dlp/Twitch ffmpeg, small test additions and import refactors.